I have done a Monte Carlo with a CFA model for categorical data. The estimation is WLSMV. Below are my questions:
1. It turns out the empirical chi-square does not match the theoretical chi-square well, but the RMSEA percentiles matches well for values beyond the median. My impression is that RMSEA can be calculated from the chi square, so the two statistics are just transformation of each other. In this case, should the Monte Carlo conclusions regarding the two be the same? In particular, I found the empirical percentiles between RMSEA and chi square are desired transformations of each other, but the theoretical percentiles are not. Why is this the case?
2. The theoretical percentiles of RMSEA involves negative numbers. Why?
3. Is it possible to perform Monte Carlo on a difference test with WLSMV?